Most bills (for outstanding payments) will have a sort code (6 digits with hyphens, like nn-nn-nn) followed by an 8 digit account number, allowing payment by bank transfer. I've not looked at zipzero, but I presume that's the information it's asking for.
giffgaff doesn't send you bills for outstanding payments, because everything is prepaid. It doesn't accept bank transfers either, so you wouldn't be able to pay giffgaff through it.
